Singular Legendrian unknot links and relative Ginzburg algebras
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908592359079936 |
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| author | Asplund, Johan |
| author_facet | Asplund, Johan |
| contents | We associate to a quiver and a subquiver $(Q,F)$ a stopped Weinstein manifold $X$ whose Legendrian attaching link is a singular Legendrian unknot link $\varLambda$. We prove that the relative Ginzburg algebra of $(Q,F)$ is quasi-isomorphic to the Chekanov--Eliashberg dg-algebra of $\varLambda$. It follows that the Chekanov--Eliashberg dg-algebra of $\varLambda$ relative to its boundary dg-subalgebra, and the Orlov functor associated to the partially wrapped Fukaya category of $X$ both admit a strong relative smooth Calabi--Yau structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_03330 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Singular Legendrian unknot links and relative Ginzburg algebras Asplund, Johan Symplectic Geometry Geometric Topology Representation Theory 53D42, 53D35, 16E45 We associate to a quiver and a subquiver $(Q,F)$ a stopped Weinstein manifold $X$ whose Legendrian attaching link is a singular Legendrian unknot link $\varLambda$. We prove that the relative Ginzburg algebra of $(Q,F)$ is quasi-isomorphic to the Chekanov--Eliashberg dg-algebra of $\varLambda$. It follows that the Chekanov--Eliashberg dg-algebra of $\varLambda$ relative to its boundary dg-subalgebra, and the Orlov functor associated to the partially wrapped Fukaya category of $X$ both admit a strong relative smooth Calabi--Yau structure. |
| title | Singular Legendrian unknot links and relative Ginzburg algebras |
| topic | Symplectic Geometry Geometric Topology Representation Theory 53D42, 53D35, 16E45 |
| url | https://arxiv.org/abs/2311.03330 |